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We assess the Value of Information (VoI) for inspecting components in systems managed by multiple agents, using game theory and Nash equilibrium analysis. We focus on binary systems made up by binary components which can be either intact or damaged. Agents taking maintenance actions are responsible for the repair costs of their own components, and the penalty for system failure is shared among all agents. The precision of inspection is also considered, and we identify the prior and posterior Nash equilibrium with perfect or imperfect inspections. The VoI is assessed for the individual agents as well as for the whole set of agents, and the analysis consider series, parallel and general systems. A negative VoI can trigger the phenomenon of Information Avoidance (IA), where rational agents prefer not to collect free information. We discuss whether it is possible that the VoI is negative for one or for all agents, for the agents with inspected or uninspected components, and for the total sum of VoIs. 

Portfolio-based algorithm selection has seen tremendous practical success over the past two decades. This algorithm configuration procedure works by first selecting a portfolio of diverse algorithm parameter settings, and then, on a given problem instance, using an algorithm selector to choose a parameter setting from the portfolio with strong predicted performance. Oftentimes, both the portfolio and the algorithm selector are chosen using a training set of typical problem instances from the application domain at hand. In this paper, we provide the first provable guarantees for portfolio-based algorithm selection. We analyze how large the training set should be to ensure that the resulting algorithm selector's average performance over the training set is close to its future (expected) performance. This involves analyzing three key reasons why these two quantities may diverge: 1) the learning-theoretic complexity of the algorithm selector, 2) the size of the portfolio, and 3) the learning-theoretic complexity of the algorithm's performance as a function of its parameters. We introduce an end-to-end learning-theoretic analysis of the portfolio construction and algorithm selection together. We prove that if the portfolio is large, overfitting is inevitable, even with an extremely simple algorithm selector. With experiments, we illustrate a tradeoff exposed by our theoretical analysis: as we increase the portfolio size, we can hope to include a well-suited parameter setting for every possible problem instance, but it becomes impossible to avoid overfitting. 

We develop a new framework for designing truth- ful, high-revenue (combinatorial) auctions for limited supply. Our mechanism learns within an instance. It generalizes and improves over previously-studied random-sampling mechanisms. It first samples a participatory group of bidders, then samples several learning groups of bidders from the remaining pool of bidders, learns a high- revenue auction from the learning groups, and fi- nally runs that auction on the participatory group. Previous work on random-sampling mechanisms focused primarily on unlimited supply. Limited supply poses additional significant technical chal- lenges, since allocations of items to bidders must be feasible. We prove guarantees on the performance of our mechanism based on a market-shrinkage term and a new complexity measure we coin par- tition discrepancy. Partition discrepancy simulta- neously measures the intrinsic complexity of the mechanism class and the uniformity of the set of bidders. We then introduce new auction classes that can be parameterized in a way that does not depend on the number of bidders participating, and prove strong guarantees for these classes. We show how our mechanism can be implemented efficiently by leveraging practically-efficient routines for solv- ing winner determination. Finally, we show how to use structural revenue maximization to decide what auction class to use with our framework when there is a constraint on the number of learning groups.